Finite Permutation Groups with Large Abelian Quotients L . G . Kovacs and Cheryl
نویسنده
چکیده
We show that if G is a group of permutations on a set of n points and if \ G/ G'\ denotes the order of its largest abelian quotient, then either \ G/ G'\ = 1 or there is a prime p dividing \ G/ G'\ such that \ G/ G'\ < p . Equality holds if and only if G is a p group which is the direct product of its transitive constituents, with each of those having order /?, except when p = 2 in which case one must also allow as transitive constituents the groups of order 4, the dihedral group of order 8 and degree 4, and the extraspecial group of order 32 and degree 8.
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تاریخ انتشار 2006